A researcher claims that a post-lunch nap decreases the amount of time it takes males to sprint 20 meters after a night with only 4 hours of sleep. The table shows the amounts of time (in seconds) it took for 10 males to sprint 20 meters after a night with only 4 hours of sleep when they did not take a post-lunch nap and when they did take a post-lunch nap. At α=0.10 is there enough evidence to support the researher's claim? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (e) below. Male 1 2 3 4 5 6 7 8 9 10 Sprint time (without nap) 3.92 4.05 4.03 4.06 4.09 3.93 4.02 4.03 3.97 4.09 Sprint time (with nap) 3.80 3.99 3.94 3.99 4.06 3.81 3.87 3.90 3.85 3.96 (a) Identify the claim and state H0 and Ha. What is the claim? A. A night with only 4 hours of sleep decreases the amount of time it takes males to sprint 20 meters. B. A night with only 4 hours of sleep increases the amount of time it takes males to sprint 20 meters. C. A post-lunch nap increases the amount of time it takes males to sprint 20 meters. D. A post-lunch nap decreases the amount of time it takes males to sprint 20 meters. Let μd be the hypothesized mean of the difference in the sprint times (without nap−with nap). What are H0 and Ha? A. H0 : μd ≠ 0 Ha : μd = 0 B. H0 : μd ≤ 0 Ha : μd > 0 C. H0 : μd = 0 Ha : μd ≠ 0 D. H0 : μd ≤ d Ha : μd > d E. H0 : μd ≥ d Ha : μd < d F. H0 :μd ≥ 0 Ha : μd < 0 (b) Find the critical value(s) and identify the rejection region(s). (Round to three decimal places as needed.) A.t < B.t < or t > C.t > (c) Calculate d and sd. d = (Round to three decimal places as needed. Calculate sd. sd = (Round to three decimal places as needed.) (d) Find the standardized test statistic t. T = (Round to three decimal places as needed.) (e) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. (Reject of fail to reject) ____ the null hypothesis. There (is not or is) ___ enough evidence to (reject or support) ___ the claim that a ( post – lunch nap or night with only 4 hours of sleep) ___ (increases or decreases) ___ the amount of time it takes males to sprint 20 meters.

A researcher claims that a post-lunch nap decreases the amount of time it takes males to sprint 20 meters after a night with only 4 hours of sleep. The table shows the amounts of time (in seconds) it took for 10 males to sprint 20 meters after a night with only 4 hours of sleep when they did not take a post-lunch nap and when they did take a post-lunch nap. At α=0.10 is there enough evidence to support the researher's claim? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (e) below. Male 1 2 3 4 5 6 7 8 9 10 Sprint time (without nap) 3.92 4.05 4.03 4.06 4.09 3.93 4.02 4.03 3.97 4.09 Sprint time (with nap) 3.80 3.99 3.94 3.99 4.06 3.81 3.87 3.90 3.85 3.96 (a) Identify the claim and state H0 and Ha. What is the claim? A. A night with only 4 hours of sleep decreases the amount of time it takes males to sprint 20 meters. B. A night with only 4 hours of sleep increases the amount of time it takes males to sprint 20 meters. C. A post-lunch nap increases the amount of time it takes males to sprint 20 meters. D. A post-lunch nap decreases the amount of time it takes males to sprint 20 meters. Let μd be the hypothesized mean of the difference in the sprint times (without nap−with nap). What are H0 and Ha? A. H0 : μd ≠ 0 Ha : μd = 0 B. H0 : μd ≤ 0 Ha : μd > 0 C. H0 : μd = 0 Ha : μd ≠ 0 D. H0 : μd ≤ d Ha : μd > d E. H0 : μd ≥ d Ha : μd < d F. H0 :μd ≥ 0 Ha : μd < 0 (b) Find the critical value(s) and identify the rejection region(s). (Round to three decimal places as needed.) A.t < B.t < or t > C.t > (c) Calculate d and sd. d = (Round to three decimal places as needed. Calculate sd. sd = (Round to three decimal places as needed.) (d) Find the standardized test statistic t. T = (Round to three decimal places as needed.) (e) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. (Reject of fail to reject) __ the null hypothesis. There (is not or is) _ enough evidence to (reject or support) _ the claim that a ( post – lunch nap or night with only 4 hours of sleep) _ (increases or decreases) ___ the amount of time it takes males to sprint 20 meters.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

α=0.10

is there enough evidence to support the researher's claim? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (e) below.

Male	1	2	3	4	5	6	7	8	9	10
Sprint time (without nap)	3.92	4.05	4.03	4.06	4.09	3.93	4.02	4.03	3.97	4.09
Sprint time (with nap)	3.80	3.99	3.94	3.99	4.06	3.81	3.87	3.90	3.85	3.96

(a) Identify the claim and state

and

Ha.

What is the claim?

A night with only 4 hours of sleep decreases the amount of time it takes males to sprint 20 meters.

A night with only 4 hours of sleep increases the amount of time it takes males to sprint 20 meters.

A post-lunch nap increases the amount of time it takes males to sprint 20 meters.

A post-lunch nap decreases the amount of time it takes males to sprint 20 meters.

Let

μd

be the hypothesized mean of the difference in the sprint times (without

nap−with

nap). What are

and

Ha?

A. H0 : μd ≠ 0 Ha : μd = 0

B. H0 : μd ≤ 0 Ha : μd > 0

C. H0 : μd = 0 Ha : μd ≠ 0

D. H0 : μd ≤ d Ha : μd > d

E. H0 : μd ≥ d Ha : μd < d

F. H0 :μd ≥ 0 Ha : μd < 0

(b) Find the critical value(s) and identify the rejection region(s).

(Round to three decimal places as needed.)

A.t <

B.t < or t >

C.t >

d = (Round to three decimal places as needed.

Calculate sd.

sd = (Round to three decimal places as needed.)

(d) Find the standardized test statistic t.

T = (Round to three decimal places as needed.)

(e) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.

(Reject of fail to reject) ____ the null hypothesis. There (is not or is) ___ enough evidence to (reject or support) ___ the claim that a ( post – lunch nap or night with only 4 hours of sleep) ___ (increases or decreases) ___ the amount of time it takes males to sprint 20 meters.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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